Questions 1 and 2 require R. You should do Questions 3 to 8 "by hand" with your calculator, then check your work in R. Submit your R code as well as your hand calculation.
Suppose you want to find a two-sided 95% confidence interval for the variance of a normal population. How many observations are needed to ensure that the upper limit is no more than 3 times the lower limit? Will this calculation be valid for non-normal data?
(a) Use R to re-draw Fig. 6.8 on p. 188 of Rosner. Make the axes, labels, tic marks, line types, legend, etc. as much like Rosner's as you can.
(b) Use R to re-draw Fig. 6.9 on p. 188 of Rosner. Make the axes, labels, tic marks, shading, etc. as much like Rosner's as you can. If c25,u = 15, as it appears to be on the graph, what is the value of u?
(c) Use R to re-draw Fig. 8.5 on p. 288 of Rosner. Make the axes, labels, tic marks, etc. as much like Rosner's as you can.
The Hamilton Spectator on 2002-04-19 reported a study where 4167 babies were classified with respect to their sex and the smoking status of their parents at time of conception. In particular, they found:
Smoking status of parents
Neither smoke Both smoke
Sex of baby boy 1975 255
girl 1627 310
Compute an odds ratio and a risk ratio. Compute a p-value to test the hypothesis that sex of baby is unrelated to smoking status of parents. State your assumptions and your conclusions
Analyse the following data sets using, as appropriate, graphical methods, the paired-data t-test, the two-sample t-test, the sign test and simple linear regression. In each case, state your assumptions and do what you can to test your assumptions.
(a) A workout area and a swimming pool were installed at a large corporate facility in an effort to lower the body mass index (BMI) of employees and hence lower the companyâs health insurance premiums. Each participantâs BMI was measured at the start of the program to get a baseline measure and again after 2 years. One employee left the company and was not available for 2-year BMI.
Subject 1 2 3 4 5 6 7 8 9 10 11 base 26.5 26.1 25.4 27.4 25.4 25.4 25.8 26.3 26.5 26.1 26.4 twoyr 26.1 26.4 25.5 26.3 NA 25.7 26.1 26.2 26.5 26.4 26.2 Subject 12 13 14 15 16 base 25.9 25.5 25.7 25.4 27.0 twoyr 26.4 25.6 24.9 25.9 26.5
(b) A creek was sampled 10 times for pH at an upstream location, where there was little human contact, and 10 times at an urban downstream location.
Down 7.20 6.99 7.41 7.30 6.59 6.78 5.93 7.00 7.62 7.86 Up 5.81 6.00 2.32 6.90 7.25 7.43 6.79 7.89 6.58 7.64
Problems 11.1-11.7 on p. 503 of Rosner. Give an appropriate graph.
Problem 12.6 on p. 568 of Rosner. Give an appropriate graph.
Analyze the following data from a study to determine the effect of 3 different poisons and 4 different antidotes on the survival time (in hours) of rats. There were 2 replicates at each combination of poison and antidote. Give a suitable graph. Give a 99% confidence interval for the residual variance. State your assumptions and your conclusions. Where possible, test your assumptions.
Antidote
A B C D
Poison I 0.31, 0.46 0.82, 0.88 0.43, 0.63 0.45, 0.66
II 0.36, 0.40 0.92, 0.49 0.44, 0.31 0.56, 0.71
III 0.22, 0.18 0.30, 0.38 0.23, 0.24 0.30, 0.31
A counselor wants to see if there is a relationship between a studentâs score on the Peabody Individual Achievement Test (PIAT) and the same studentâs score on the Wide Range Achievement Test (WRAT). He administered the reading subsets of both tests to a random sample of 10 grade 2 students on 2 consecutive days.
Student: 1 2 3 4 5 6 7 8 9 10 PIAT: 31 36 44 25 22 21 35 17 25 31 WRAT: 40 46 53 38 32 28 45 20 33 44
Fit a straight line to the data by least squares, with WRAT as the dependent variable. Plot the data and the fitted line on a graph. Can WRAT be predicted as a linear function of PIAT? Present your analysis in an ANOVA table with F-Tests for non-linearity and for the slope of the regression line. Give a 99% confidence interval for the residual variance. State your assumptions and your conclusions. Where possible, test your assumptions. What WRAT would you predict for a student who scored 30 on PIAT?